ELECTROSTATIC POTENTIAL AND CAPACITANCE
1. Electric
Potential = Work done / Charge
2. S.I Unit
of electric potential is volt.
3. 1 volt =
1 joule / 1 coulomb
4. 1 volt =
1 / 300 stat volt
5. 1 volt =
108 ab volt
6. Electric
potential (v) = 1/4πϵ0 (q
/ r)
7. V α 1 / r
8. V axial
= 1/4πϵ0 (p / r2)
9. V equatorial = 0
10. Electric potential due to a uniformly charged thin spherical shell:
V out = 1/4πϵ0 (q / r)
V in =
1/4πϵ0 (q / R)
V surface
= 1/4πϵ0 (q / R)
11. E = - dV / dr
Here dV / dr is the rate of change of
potential with distance and is called potential gradient.
12. V (r) = -ʃr∞ E. dr
13. S.I. unit of E = Volt / metre
14. Properties of equipotential surfaces:
o
No work is done
in moving a test charge over an equipotential surface.
o
Electric field is
always normal to equipotential surface at every point.
o
Equipotential
surfaces are closer together in the regions of strong field and farther apart
in the regions of weak field.
o
No two
equipotential surfaces can intersect each other.
15. P.E. of a charge in an external
field = charge x external electric potential
16. Units of electrostatic potential
energy is electron volt (eV).
17. 1 eV = 1.6 x 10-19 joule
18. 1 MeV = 1.6 x 10-13 joule
19. C = Q / V
Here C = Capacitance
Q = charge
V= Potential
20. The capacitance depends upon following factors:
§ Size and shape of conductor
§ Permittivity of the surrounding medium
§ Presence of the other conductors in its
neighbourhood
21. S.I. unit of capacitance is farad.
22. 1 farad = 1 coulomb / 1 volt
23. 1 millifarad = 1mF = 10-3 farad
24. 1 microfarad = 1µF = 10-6
farad
25. 1 nanofarad = 1 nF = 10-9
farad
26. 1 picofarad = 1 pF = 10-12
farad
27. Capacitance of an isolated spherical capacitor:
§ C = 4πϵ0R = R / 9 x 109 [ When C & R are in S.I. units ]
Here C =
capacitance
R = Radius
§ C = R [ When C & R are in
C.G.S. units ]
28.
Parallel plate capacitor –
C = ϵ0 A / d
Here ϵ0 = Permittivity of
free space
A = Area of plates
d = Distance between the plates
29. Factors on which the capacitance of a parallel plate capacitor depends:
§ Area of plates
§ Distance between the plates
§ Permittivity of medium between the plates
30. When a dielectric of dielectric
constant ‘K’ introduce between two plates, the capacitance of a parallel plate
capacitor increases k times. Then capacitance becomes
C = ϵ0 K A /
d
Here K = Dielectric constant
31. Capacitors in series –
When
the negative plate of one capacitor is connected to the positive plate of
second and the negative of the second to the positive of third and so on, the
capacitors are said to be connected in series.
|| || ||
C 1 C 2 C 3
1 / Cs = 1 /C 1 +
1 / C 2 + ………….. + 1 / C n
§ The charge on each capacitors is same.
§ The equivalent capacitance is smaller than the
smallest individual capacitance.
32. Capacitors in parallel –
When
the positive plates of all capacitors are connected to one common point and the
negative plates to another common point, the capacitance are said to be
connected in parallel.
||
||
C
p = C1 + C 2 + …………. + C n
§ The equivalent capacitance is larger
than the largest individual capacitance.
§ The potential difference across each
capacitor is same.
33. Energy stored in a capacitor –
U = 1 / 2 [Q2 / C] = 1 / 2
(C V2) = 1 / 2 (QV)
34. The polarization
P is defined as a dipole moment per
unit volume.
35. Uses of Capacitor –
§ In radio circuit for tuning.
§ In power supplies for smoothing the
rectified current.
§ In the tank circuit of oscillators.
§ For producing rotating magnetic
fields in induction motors.
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